They will certainly say they do. However, they don't generally behave as if they really truly deep down believe that. In particular, I can think of very few occasions when I have seen Christians acting more motivated by the prospect of heavenly rewards than they would have been by an offer of $1M in a year's time.

A certain ilk of Christians do behave in ways that indicate they are very motivated by heavenly rewards. Some do not. Some believe a divine tally sheet doesn't exist. Some believe it is very real and act accordingly. Some say they believe in rewards but there is no evidence indicating that stated belief is sincere. I've met all kinds.

Note also that a typical Christian facing an injured biker probably doesn't believe that he will be saved if he helps and damned if he doesn't, Matthew 25:31ff notwithstanding. Quite right, too; after all, he will be faced with plenty of other opportunities to help or not help, and it can't possibly be true that each of them determines whether he's saved or damned.

True, except I have met Christians who believe that unrepentant sin could lead to hell, and that Matt 25:31 will describe the fate of many, many of the alleged "saved". In this way, the bold is not necessarily true, as God may rapture at an inopportune time and leave a Christian who has recently turned up her nose at a bloodied biker deserving of hell.

And note also-also that this isn't really about Christians versus everyone else; it's about people who believe in huge post-mortem rewards and punishments versus everyone else. E.g., Muslims' beliefs on this score are broadly similar to Christians'.

Noted.